report0411

Hi Professor,

This document is to show my problem in finding the parametric approximation of the loglikelihood function.

One known fact:

• when the length of data double, the loglikelihood double(other parameters are the same)

where the x-axis is the irregular variance; the black line is the loglikelihood of one dataset at length 30 years, red line is the loglikelihood of the first 15 years, blue line is taking one half of the black line

length2

where the x-axis is the trend variance; the black line is the loglikelihood of one dataset at length 30 years, red line is the loglikelihood of the first 15 years, blue line is taking one half of the black

The 3D distribution of the loglikelihood is:(it may take some time to load the figure)